Abstract
Interactive Markov chains (IMCs) are powerful models of concurrent systems, and branching time equivalences are useful to compare the behaviour of concurrent systems. In this paper we define various branching time relations on IMCs, including strong and weak (bi)simulations, and investigate connections among these relations. These relations are defined as an orthogonal extensions of classical labelled transition systems and pure stochastic settings. The logical characterizations of them are also studied by using an action-based logic aCSL. We show that for IMCs, bisimulation equivalence coincides with aCSL-equivalence, and simulation preorder weakly preserves aCSL safety and liveness formulae.
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Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Verifying continuous time Markov chains. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 269–276. Springer, Heidelberg (1996)
Aziz, A., Singhal, V., Balarin, F., Brayton, R., Sangiovanni-Vincentelli, A.: It usually works: the temporal logic of stochastic systems. In: Wolper, P. (ed.) CAV 1995. LNCS, vol. 939, pp. 155–165. Springer, Heidelberg (1995)
Baier, C., Katoen, J.-P., Hermanns, H., Haverkort, B.: Simulation for continuoustime Markov chains. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 338–354. Springer, Heidelberg (2002)
Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P.: Model checking continuous-time Markov chains by transient analysis. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 358–372. Springer, Heidelberg (2000)
Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P.: On the logical characterization of performability properties. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 780–792. Springer, Heidelberg (2000)
Baier, C., Katoen, J.-P., Hermanns, H.: Approximate symbolic model checking of continuous-time Markov chains. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 146–162. Springer, Heidelberg (1999)
Baier, C., Hermanns, H., Katoen, J.-P., Wolf, V.: Comparative branchingtime semantics for Markov chains. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 492–507. Springer, Heidelberg (2003)
Baier, C., Hermanns, H.: Weak bisimulation for fully probabilistic processes. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 119–130. Springer, Heidelberg (1997)
Bravetti, M.: Revisiting Interactive Markov Chains. 3rd Workshop on Models for Time-Critical Systems, BRICS Notes NP-02-3, pp. 68–88 (2002)
Brown, M., Clarke, E., Grumberg, O.: Characterizing finite Kripke structures in propositional temporal logic. Th. Comp. Sci. 59, 115–131 (1988)
Clarke, E., Grumberg, O., Long, D.E.: Model checking and abstraction. ACM Trans. on Programming Language and Systems 16(5), 1512–1542 (1994)
Desharnais, J.: Logical characterisation of simulation for Markov chains. In: Proc. Workshop on Probabilistic Methods in Verification, Tech. Rep. CSR-99-8, Univ. of Birmingham (1999)
Desharnais, J., Panangaden, P.: Continuous stochastic logic characterizes bisimulation of continuous-time Markov processes. J. of Logic and Algebraic Programming (2003)
van Glabbeek, R.: The linear time - branching time spectrum I. The semantics of concrete, sequential processe. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1989. LNCS, vol. 430, pp. 267–300. Springer, Heidelberg (1990)
van Glabbeek, R.: The linear time - branching time spectrum II. The semantics of sequential processes with silent moves. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 66–81. Springer, Heidelberg (1993)
Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Form. Asp. of Comp. 6, 512–535 (1994)
Hermanns, H.: Interactive Markov Chains. PhD thesis, Universität Erlangen- Nürnberg (1998)
Hermanns, H., Katoen, J.-P., Meyer-Kayser, J., Siegle, M.: Towards model checking stochastic process algebra. In: Grieskamp, W., Santen, T., Stoddart, B. (eds.) IFM 2000. LNCS, vol. 1945, pp. 420–439. Springer, Heidelberg (2000)
Jonsson, B., Larsen, K.G.: Specifcation and refnement of probabilistic processes. In: IEEE Symp. on Logic in Computer Science, pp. 266–277 (1991)
Jonsson, B.: Simulations between specifications of distributed systems. In: Groote, J.F., Baeten, J.C.M. (eds.) CONCUR 1991. LNCS, vol. 527, pp. 346–360. Springer, Heidelberg (1991)
Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)
De Nicola, R., Vaandrager, F.: Three logics for branching bisimulation. J. of ACM 42(2), 458–487 (1995)
Segala, R., Lynch, N.A.: Probabilistic simulations for probabilistic processes. Nordic J. of Computing 2(2), 250–273 (1995)
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Qin, G., Wu, J. (2004). Branching Time Equivalences for Interactive Markov Chains. In: Núñez, M., Maamar, Z., Pelayo, F.L., Pousttchi, K., Rubio, F. (eds) Applying Formal Methods: Testing, Performance, and M/E-Commerce. FORTE 2004. Lecture Notes in Computer Science, vol 3236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30233-9_12
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DOI: https://doi.org/10.1007/978-3-540-30233-9_12
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